Equilibrium Concentrations at a Certain Temperature and Pressure: Varying Reaction Coefficients

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Equilibrium Concentrations at a Certain Temperature and Pressure: Varying Reaction Coefficients

13.10. Peter, Paul, and Mary, members of a thermodynamics class, are asked to find the equilibrium composition at a particular T and P and for given initial amounts of reactants for the following gas-phase reaction:
2NH3 + 3NO -> 3H2O + 5/2 N2 (A)
Each solves the problem correctly in a different way. Mary bases her solution on reaction (A) as written. Paul, who prefers whole numbers, multiplies reaction (A) by 2:
4NH3 + 6N0 -> 6H20 + 5N2 (B)
Peter, who usually does things backward, deals with the reaction:
3H2O + 5/2 N2 -> 2NH3 + 3NO (C)
Write the chemical-equilibrium equations for the three reactions, indicate how the equilibrium constants are related, and show why Peter, Paul, and Mary all obtain the same result.